论文标题
在晶格上相同玻色子合奏的功能积分和随机表示
Functional Integral and Stochastic Representations for Ensembles of Identical Bosons on a Lattice
论文作者
论文摘要
正则化相干状态功能积分是针对晶格上相同玻色子的集合得出的，正则化是欧几里得时间的离散化。为各种离散的动作显示了时间限制限制的收敛性。重点放在规范集合中分区函数和期望值的积分表示上。讨论了与大型典型积分和许多差异的联系。证明了协方差的统一边界，这简化了对时间限制的分析，也可以用于分析热力学极限。通过相互作用的随机步行集合的合奏与随机表示的关系是明确的，并讨论了在凝结物存在下的修改。
Regularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being a discretization of Euclidian time. Convergence of the time-continuum limit is shown for various discretized actions. The focus is on the integral representation for the partition function and expectation values in the canonical ensemble. The connection to the grand-canonical integral, and a number of differences, are discussed. Uniform bounds for covariances are proven, which simplify the analysis of the time-continuum limit and can also be used to analyze the thermodynamic limit. The relation to a stochastic representation by an ensemble of interacting random walks is made explicit, and its modifications in presence of a condensate are discussed.
